Zero-Order Instruments notes by kanyai tt.pptx

Notes

1. Zero-Order Instruments By Kanyai Tapiwa T

2. KEY POINTS What is a Zero-Order Instrument Mathematical model Key Characteristics Real-World Examples Advantages and Limitations

3. Definition Output instantly follows the input ( no time lag or distortion) It is the simplest model in measurement systems

4. Mathematical model Governing Equation x o (t) = K x i (t) K: static senstitivity (measure of change in instrument output when quantity being measured changes by a given amount) > From the equation it is apparent that the output x o faithfully follows input x i without distortion or time lag of any sort

5. Block diagram

6. Key characteristics Useful for static inputs (dynamic signals can only be measured at equilibrium conditions) Step response: output changes abruptly in response to change in input ideal dynamic performance, because the output is proportional to the input for all frequencies and there is no amplitude or phase distortion

7. Example: Potentiometer Voltage output is proportional to wiper position the output voltage changes instantaneously as the slider is displaced along the potentiometer track.

8. Zero order vs First Order Zero order first order No energy storage contains one storage element eg capacitor Used for static measurements eg potentiometers Suitable for time varying signals where slight delays are tolerable eg thermometers Step response Output approaches a steady value exponentially

9. advantages Simple design : minimal components eg resistors Low cost Fast response: suitable for applications where fast response time is critical No dynamic error : perfect for static/ low-frequency signals

10. limitations Cannot capture dynamics : fail for time varying/high frequency signals Real-word deviations :parasitic effects eg inductance in resistors, wiring capacitance or material inertia which introduce delays Requires frequent calibration

11. Comprehension check Summarize the defining characteristic of a zero-order instrument

12. Possible answer Has an output that responds instantaneously to input with no time delay